Given $ m \angle BOC = 6x + 7$, and $ m \angle AOB = 5x - 14$, find $m\angle BOC$. $O$ $A$ $C$ $B$
From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {5x - 14} + {6x + 7} = {180}$ Combine like terms: $ 11x - 7 = 180$ Add $7$ to both sides: $ 11x = 187$ Divide both sides by $11$ to find $x$ $ x = 17$ Substitute $17$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 6({17}) + 7$ Simplify: $ {m\angle BOC = 102 + 7}$ So ${m\angle BOC = 109}$.